The half-life of uranium-235 is 700,000,000 years. The half-life of uranium-238 is 4.463×1011 years longer. What is the half-life of uranium-238? The answer should be in decimal form.(1 point)

Question

Responses

4.4637×1011
4.4637 times 10 superscript 11 baseline

516,300,000,000
516,300,000,000

11,463,000,000
11,463,000,000

447,000,000,000

Answer 1

To find the half-life of uranium-238, we need to add the half-life of uranium-235 to the additional duration given for uranium-238.

1. The half-life of uranium-235 is \( 700,000,000 \) years.
2. The half-life of uranium-238 is \( 4.463 \times 10^{11} \) years longer than that of uranium-235.

Calculating this:

\[ \text{Half-life of uranium-238} = 700,000,000 + 4.463 \times 10^{11} \]

First, convert \( 700,000,000 \) into scientific notation:

\[ 700,000,000 = 7.0 \times 10^8 \]

Now, we need to express both values in the same order of magnitude in order to add them:

\[ 4.463 \times 10^{11} = 446.3 \times 10^9 \] (We can express \( 4.463 \) as \( 446.3 \), but we lose \( 10^2 = 100 \). Now we have to express \( 700,000,000 = 7.0 \times 10^8 \) in terms of \( 10^9 \):)

\[ 7.0 \times 10^8 = 0.7 \times 10^9 \]

Now we can add the two half-lives together:

\[ \text{Half-life of uranium-238} = 0.7 \times 10^9 + 446.3 \times 10^9 = (0.7 + 446.3) \times 10^9 = 447.0 \times 10^9 \]

Converting \( 447.0 \times 10^9 \) back into decimal form, we get:

\[ 447,000,000,000 \text{ years} \]

Thus, the half-life of uranium-238 is:

447,000,000,000